"The President has been awol on this," Scalise, the newly elected House Majority Whip, said on "Fox News Sunday." "Ultimately, this is the president's responsibility."

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"The president has a lot of time to secure fundraisers, but no time to secure the border. He wants to sit back and play politics but hasn't had time to come and sit down with Congress," Scalise said of Obama's recent fundraising events for Democrats facing reelection.

The House is considering legislation it plans to move on during the final week before August recess.

When asked if the House GOP might postpone its summer break to deal with securing the border and work on a compromise, Scalise wouldn't be pinned down.

Instead, when pressed multiple times on whether the House would stay in Washington, D.C., going into August, Scalise said the House "wants to keep working" on legislation to address the border.